Recent work claims that large language models display \textit{emergent abilities}, abilities not present in smaller-scale models that are present in larger-scale models.What makes emergent abilities intriguing is two-fold: their \textit{sharpness}, transitioning seemingly instantaneously from not present to present, and their \textit{unpredictability}, appearing at seemingly unforeseeable model scales.Here, we present an alternative explanation for emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due the researcher's choice of metric rather than due to fundamental changes in model behavior with scale. Specifically, nonlinear or discontinuous metrics produce apparent emergent abilities, whereas linear or continuous metrics produce smooth, continuous, predictable changes in model performance.We present our alternative explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities, (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on BIG-Bench; and (3) show how to choose metrics to produce never-before-seen seemingly emergent abilities in multiple vision tasks across diverse deep networks.Via all three analyses, we provide evidence that alleged emergent abilities evaporate with different metrics or with better statistics, and may not be a fundamental property of scaling AI models.

Recent studies have put into question the belief that emergent abilities in language models are exclusive to large models. This skepticism arises from two observations: 1) smaller models can also exhibit high performance on emergent abilities and 2) there is doubt on the discontinuous metrics used to measure these abilities. In this paper, we propose to study emergent abilities in the lens of pre-training loss, instead of model size or training compute. We demonstrate that the Transformer models with the same pre-training loss, but different model and data sizes, generate the same performance on various downstream tasks, with a fixed data corpus, tokenization, and model architecture. We also discover that a model exhibits emergent abilities on certain tasks--regardless of the continuity of metrics--when its pre-training loss falls below a specific threshold. Before reaching this threshold, its performance remains at the level of random guessing. This inspires us to redefine emergent abilities as those that manifest in models with lower pre-training losses, highlighting that these abilities cannot be predicted by merely extrapolating the performance trends of models with higher pre-training losses.

How do different metrics behave when used to measure autoregressive model outputs? A.1 Per-T oken Error Probability is Resolution-Limited Here, resolution refers to "the smallest interval measurable After F coin flips, we can only resolve the coin's probability of A.3), we ignore how likely the language model is to over-348 Section 3.2 of [23] gives the exact definition, but the Simulations show that as the per-token error probability slightly increase (e.g. from 0.05 to 0.1), the ROUGE-L-Sum metric sharply falls.Figure 10: Induced emergent MNIST classification ability in convolutional networks.

Phase transitions have been proposed as the origin of emergent abilities in large language models (LLMs), where new capabilities appear abruptly once models surpass critical thresholds of scale. Prior work, such as that of Wei et al., demonstrated these phenomena under model and data scaling, with transitions revealed after applying a log scale to training compute. In this work, we ask three complementary questions: (1) Are phase transitions unique to large models, or can they also be observed in small transformer-based language models? (2) Can such transitions be detected directly in linear training space, rather than only after log rescaling? and (3) Can these transitions emerge at early stages of training? To investigate, we train a small GPT-style transformer on a character-level corpus and analyze the evolution of vocabulary usage throughout training. We track the average word length, the number of correct versus incorrect words, and shifts in vocabulary diversity. Building on these measures, we apply Poisson and sub-Poisson statistics to quantify how words connect and reorganize. This combined analysis reveals a distinct transition point during training. Notably, these transitions are not apparent in standard loss or validation curves, but become visible through our vocabulary- and statistics-based probes. Our findings suggest that phase-transition reorganizations are a general feature of language model training, observable even in modest models, detectable directly in linear training space, and occurring surprisingly early as coherence emerges. This perspective provides new insight into the nonlinear dynamics of language model training and underscores the importance of tailored metrics for uncovering phase transition behaviors

In this paper, we propose to study emergent abilities in the lens of pre-training loss, instead of model size or training compute.

How do different metrics behave when used to measure autoregressive model outputs? A.1 Per-T oken Error Probability is Resolution-Limited Here, resolution refers to "the smallest interval measurable After F coin flips, we can only resolve the coin's probability of A.3), we ignore how likely the language model is to over-348 Section 3.2 of [23] gives the exact definition, but the Simulations show that as the per-token error probability slightly increase (e.g. from 0.05 to 0.1), the ROUGE-L-Sum metric sharply falls.Figure 10: Induced emergent MNIST classification ability in convolutional networks.

Here, we present an alternative explanation for emergent abilities: for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due to the researcher's choice of metric rather than due to fundamental changes in models with scale.

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.