A Theory of LLM Information Susceptibility

Abstract

Large language models (LLMs) are increasingly deployed as optimization modules in agentic systems, yet the fundamental limits of such LLM-mediated improvement remain poorly understood. Here we propose a theory of LLM information susceptibility, centred on the hypothesis that when computational resources are sufficiently large, the intervention of a fixed LLM does not increase the performance susceptibility of a strategy set with respect to budget. We develop a multi-variable utility-function framework that generalizes this hypothesis to architectures with multiple co-varying budget channels, and discuss the conditions under which co-scaling can exceed the susceptibility bound. We validate the theory empirically across structurally diverse domains and model scales spanning an order of magnitude, and show that nested, co-scaling architectures open response channels unavailable to fixed configurations. These results clarify when LLM intervention helps and when it does not, demonstrating that tools from statistical physics can provide predictive constraints for the design of AI systems. If the susceptibility hypothesis holds generally, the theory suggests that nested architectures may be a necessary structural condition for open-ended agentic self-improvement.

Figures (9)

• Figure 1: Framework and representative results. Performance $J$ (lines cleared) versus computational budget $\mathcal{B}$ (beam width) in the Tetris domain for the base algorithm (DFS, blue circles) and LLM-derived strategies (red markers; five Qwen models: 7B, 14B, 32B, 72B and Qwen3-Max). Dashed lines show linear fits for DFS and the LLM average. Error bars indicate the standard error of the mean across 40 random seeds. The schematic on the right illustrates the two evaluation paths: the base strategy set $\mathcal{P}_\mathcal{B}$ is evaluated directly by the utility function $J$ (base path, blue), or first processed by a fixed LLM to produce a derived set $\mathcal{P}'_\mathcal{B}$ (derived path, red).
• Figure 2: Robustness of the susceptibility bound.a, Four prompt variants compared against the DFS baseline in the Tetris domain (Qwen-32B). The minimal prompt nearly matches DFS at high $\mathcal{B}$, while more elaborative prompts amplify the gap. b, Three reward functions overlaid for both DFS (grey shades) and LLM (red shades, Qwen-32B). The susceptibility bound holds across all prompt and reward configurations.
• Figure 3: Transition of the relative sensitivity $\alpha$. Average $\alpha$ versus the number of samples $k$. For each $k$, $\alpha$ is estimated by fitting $J_\mathrm{agent} = \alpha \cdot J_\mathrm{MV} + \beta$ across five generator model sizes, where $J_\mathrm{MV}$ is the majority-vote accuracy, $J_\mathrm{agent}$ is the LLM-selector accuracy and $\beta$ is the regression intercept (see Methods). As $k$ increases, $\alpha$ decreases and falls below 1 around $k \sim 12$, marking the onset of the large-budget regime where the susceptibility bound takes effect.
• Figure 4: Cross-domain validation. Performance $J$ versus computational budget $\mathcal{B}$ for the base strategy set (blue circles) and the LLM-derived strategy set (red squares) across four domains: Tetris, Knapsack, Ranking and AIME mathematics. In the AIME domain, the derived strategy set averages over all five selector models and over $k \in \{15, 17, 19, 21\}$.
• Figure 5: Inter-layer coupling regimes. Each panel shows an architecture diagram (top) and illustration of $J$ versus $\mathcal{B}_\mathrm{ref}$ (bottom). Faded blue lines represent three fixed-selector configurations; solid coloured lines show the nested (co-scaled) configuration. Dots mark intersection points where configurations coincide. a, Decoupled: only the generator scales with $\mathcal{B}_\mathrm{ref}$; the selector remains fixed. The nested line coincides with one of the fixed lines. b, Negative coupling: both components scale, but co-scaling reduces marginal return ($\alpha_\mathrm{total} < 1$). The nested line falls below the fixed line. c, Positive coupling: co-scaling amplifies marginal return ($\alpha_\mathrm{total}$ can exceed 1). The nested line exceeds all fixed lines, opening a response channel unavailable to fixed architectures.