Recent research into large language models (LLMs) has revealed fascinating patterns in how these systems develop capabilities. While initial discussions of "emergent abilities" suggested sudden, discontinuous jumps in performance, closer analysis reveals a more nuanced picture that warrants careful examination.

The Data Behind Emergence

The concept of emergence in LLMs was first systematically studied through the BIG-bench benchmark. Initial observations suggested that capabilities like emoji movie interpretation appeared to emerge suddenly at certain model scales. For instance, between 10^10 and 10^11 parameters, models showed dramatic improvements in their ability to interpret emoji sequences representing movies.

However, these apparent discontinuities deserve closer scrutiny. When we examine the actual data:

1. The choice of evaluation metric significantly impacts whether abilities appear emergent. When using exact string matching, capabilities seem to appear suddenly. However, when using multiple-choice evaluations or examining log likelihoods of correct answers, we see much more gradual improvements.
2. Looking at aggregate performance across benchmarks (as seen in GPT-3's development), the improvement curves are actually smooth rather than discontinuous.

Understanding Multi-Step Reasoning

One compelling explanation for apparently emergent behavior comes from examining multi-step reasoning. Consider a task requiring ten consecutive correct reasoning steps. Even if a model's ability to perform individual reasoning steps improves smoothly, the probability of completing the entire chain successfully can show a sharp, seemingly discontinuous jump.

This matches what we observe in practice. Tasks requiring multiple steps of reasoning or complex chains of thought tend to show more apparent "emergence" than simpler tasks, even though the underlying capabilities may be improving gradually.

Scaling Laws and Practical Limitations

Recent research from Google DeepMind (the Chinchilla paper) has shown that optimal training requires about 20 tokens of training data for each parameter in the model. This creates practical limits on scaling:

• A 100-trillion parameter model would require approximately 2,000 trillion tokens of training data
• This would need about 180 petabytes of high-quality text
• For comparison, the entire Common Crawl dataset is only about 12 petabytes

These constraints help explain why we haven't seen models scaled to the size that early GPT-4 rumors suggested (100T parameters). The limiting factor isn't just compute - it's the availability of quality training data.

Implications for AI Development

This more nuanced understanding of emergence has important implications:

1. What appears as sudden emergence may often be the product of smoothly improving underlying capabilities crossing human-relevant thresholds.
2. We should be cautious about extrapolating from apparent discontinuities, as they may be artifacts of our evaluation methods rather than fundamental properties of the models.
3. The practical limits on scaling suggest that qualitative improvements in architecture and training efficiency may be more important than raw scale for future advances.

Moving Forward

Rather than focusing on emergence as a mysterious phenomenon, we should:

1. Develop better evaluation metrics that capture gradual improvements in capability
2. Create hierarchical maps of model capabilities to understand dependencies between different abilities
3. Focus on improving training efficiency to make better use of available data
4. Study how architectural improvements might lead to better performance without requiring exponential increases in scale

The development of LLM capabilities is more predictable than initial observations suggested, but this makes the field no less fascinating. Understanding these patterns helps us better predict and guide the development of these powerful systems.