Bound by semanticity: universal laws governing the generalization-identification tradeoff

Intelligent systems must deploy internal representations that are simultaneously structured -- to support broad generalization -- and selective -- to preserve input identity. We expose a fundamental limit on this tradeoff. For any model whose representational similarity between inputs decays with finite semantic resolution $\varepsilon$, we derive closed-form expressions that pin its probability of correct generalization $p_S$ and identification $p_I$ to a universal Pareto front independent of input space geometry. Extending the analysis to noisy, heterogeneous spaces and to $n>2$ inputs predicts a sharp $1/n$ collapse of multi-input processing capacity and a non-monotonic optimum for $p_S$. A minimal ReLU network trained end-to-end reproduces these laws: during learning a resolution boundary self-organizes and empirical $(p_S,p_I)$ trajectories closely follow theoretical curves for linearly decaying similarity. Finally, we demonstrate that the same limits persist in two markedly more complex settings -- a convolutional neural network and state-of-the-art vision-language models -- confirming that finite-resolution similarity is a fundamental emergent informational constraint, not merely a toy-model artifact. Together, these results provide an exact theory of the generalization-identification trade-off and clarify how semantic resolution shapes the representational capacity of deep networks and brains alike.

@article{nurisso2025_2506.14797,
  title={ Bound by semanticity: universal laws governing the generalization-identification tradeoff },
  author={ Marco Nurisso and Jesseba Fernando and Raj Deshpande and Alan Perotti and Raja Marjieh and Steven M. Frankland and Richard L. Lewis and Taylor W. Webb and Declan Campbell and Francesco Vaccarino and Jonathan D. Cohen and Giovanni Petri },
  journal={arXiv preprint arXiv:2506.14797},
  year={ 2025 }
}