Emergent Capabilities as Universal Latent Modes

Emergent capabilities in large language models — abilities that appear suddenly as model scale increases — remain poorly understood. We propose that emergence corresponds to the activation of new universal Latent modes: directions in the model's representation space that are shared across all domains. Using the Latent of Latents framework (Nagy 2026h), we decompose a model's knowledge into domain-specific variation (captured by centered meta-axes) and universal variation (captured by the non-centered mean component). Each new universal mode represents a cross-domain capability — summarization, reasoning, analogy — that the model has learned to apply uniformly.

Preliminary evidence from GPT-2 Small (1 universal mode, 99.6% of universal variance) and TinyLlama 1.1B (2–3 universal modes, 67% + 3.5% + 0.8%) shows that larger models develop more universal modes, consistent with the emergence of new cross-domain capabilities at scale. We propose a tri-graded Latent algebra \(\Lambda^{(i,j,k)}\) where \(i\) = within-domain, \(j\) = across-domain, \(k\) = universal depth, and predict that the number of universal modes at threshold \(\varepsilon\) scales as \(K_\varepsilon \sim \log \log P\) where \(P\) is parameter count.