Why are LLMs' abilities emergent?

Abstract: The remarkable success of Large Language Models (LLMs) in generative tasks has raised fundamental questions about the nature of their acquired capabilities, which often appear to emerge unexpectedly without explicit training. This paper examines the emergent properties of Deep Neural Networks (DNNs) through both theoretical analysis and empirical observation, addressing the epistemological challenge of "creation without understanding" that characterises contemporary AI development. We explore how the neural approach's reliance on nonlinear, stochastic processes fundamentally differs from symbolic computational paradigms, creating systems whose macro-level behaviours cannot be analytically derived from micro-level neuron activities. Through analysis of scaling laws, grokking phenomena, and phase transitions in model capabilities, I demonstrate that emergent abilities arise from the complex dynamics of highly sensitive nonlinear systems rather than simply from parameter scaling alone. My investigation reveals that current debates over metrics, pre-training loss thresholds, and in-context learning miss the fundamental ontological nature of emergence in DNNs. I argue that these systems exhibit genuine emergent properties analogous to those found in other complex natural phenomena, where systemic capabilities emerge from cooperative interactions among simple components without being reducible to their individual behaviours. The paper concludes that understanding LLM capabilities requires recognising DNNs as a new domain of complex dynamical systems governed by universal principles of emergence, similar to those operating in physics, chemistry, and biology. This perspective shifts the focus from purely phenomenological definitions of emergence to understanding the internal dynamic transformations that enable these systems to acquire capabilities that transcend their individual components.