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.
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Figure 1: Framework and representative results. Performance J (lines cleared) versus computational budget 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 PB is evaluated directly by the utility function J (base path, blue), or first processed by a fixed LLM to produce a derived set PB′ (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 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 α . Average α versus the number of samples k . For each k , α is estimated by fitting Jagent=α⋅JMV+β across five generator model sizes, where JMV is the majority-vote accuracy, Jagent is the LLM-selector accuracy and β is the regression intercept (see Methods). As k increases, α decreases and falls below 1 around k∼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 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∈{15,17,19,21} .
Figure 5: Inter-layer coupling regimes. Each panel shows an architecture diagram (top) and illustration of J versus Bref (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 Bref ; 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 ( αtotal<1 ). The nested line falls below the fixed line. c , Positive coupling: co-scaling amplifies marginal return ( αtotal can exceed 1). The nested line exceeds all fixed lines, opening a response channel unavailable to fixed architectures.
Figure 6: Nested versus fixed architectures in the AIME domain. Accuracy J (averaged over k∈{15,17,19,21} ) versus model size for the nested derived strategy set (generator and selector co-scaled) and fixed derived strategy sets (fixed selector, varying generator). The curves intersect at the model size of the respective fixed selector, showing that co-scaling architectural components can exceed the susceptibility bound.
Extended Data Fig. 1 ∣ Averaged performance gap across domains. The normalized performance gap Δ(B)=(J(PB)−J(PB′))/J(PB) , averaged over all five LLMs, as a function of computational budget B for four domains. Blue shading indicates the regime where the base algorithm outperforms the LLM-derived strategy ( Δ>0 ); red shading indicates the opposite. In Tetris, Δ grows monotonically. In Knapsack, Δ is negligible. In Ranking, Δ transitions from negative (LLM advantage at low SNR) to near zero. In AIME, Δ (averaged over k∈{15,17,19,21} ) remains positive across model sizes.
Extended Data Fig. 2 ∣ Per-model performance gap across domains. The normalized performance gap Δ(B) broken down by individual model size (7B through Qwen3-Max) for each domain. In Tetris, 72B models show largest gaps. In Knapsack, all models produce negligible gaps. In Ranking, all models converge from negative to near-zero Δ as SNR increases. In AIME, the gap varies with both generator model size and number of samples k , with larger k showing an increasing tendency with model size.
Extended Data Fig. 3 ∣ Illustration of the phenomenological theory of self-evolution dynamics. Top row: data quality functions p(b) (pipeline, blue) and l(b) (model output, red) versus model capability b . Bottom row: phase portrait db/dr∝p(b)−l(b) , with arrows indicating the flow direction. Open circle: unstable fixed point; filled circle: stable fixed point. a , p′(b)>l′(b) : the fixed point is a repeller, giving rise to a collapse phase ( b<b∗ ) and a self-evolution phase ( b>b∗ ). b , p′(b)<l′(b) : the fixed point is an attractor; improvement and degradation are both bounded. See Supplementary Note 1 for the full derivation.