当我们谈论人工智能（AI），尤其是近年来ChatGPT这类大型语言模型（LLM）带来的震撼时，背后有一个深刻的规律在默默支撑着这一切的进步，它就是由OpenAI研究员贾里德·卡普兰（Jared Kaplan）及其团队在2020年提出的“卡普兰缩放定律”（Kaplan Scaling Law），也常被称为“缩放定律”的一部分。这项定律揭示了AI模型性能提升的“奥秘”，让我们能以一种前所未有的方式，预测和引导AI的发展。
什么是“卡普兰缩放定律”？—— AI世界的“增长秘籍”
想象一下，你正在为一场大型烹饪比赛做准备。为了做出最美味的菜肴，你需要考虑几个关键因素：
- 厨师的能力（模型大小）：一个经验丰富的厨师（参数量多的模型）通常能做出更复杂的菜肴，处理各种食材。
- 食材的品质和数量（数据集大小）：再好的厨师，没有足够多、足够新鲜的食材（高质量、大规模的数据），也巧妇难为无米之炊。
- 厨房的设备和投入的时间（计算资源）：拥有顶级设备、充足时间去练习和调试，才能充分发挥厨师的技艺（高算力、长时间的训练）。
“卡普兰缩放定律”就好像是这个烹饪比赛的“增长秘籍”，它指出，AI模型的性能（例如，模型犯错的概率或者理解语言的能力）并非是随机提升的，而是与这三个核心因素——模型大小（参数量）、数据集大小和训练所消耗的计算资源——之间存在着一种可预测的、幂律（power law）关系。简单来说，只要我们持续地、有策略地增加这三个“投入”，AI模型的性能就会以可预测的方式持续提升。
贾里德·卡普兰本人曾是一名理论物理学家，他用物理学家的严谨视角审视AI，发现AI的发展也遵循着如同物理学定律般精确的数学规律，仿佛找到了AI领域的“万有引力定律”。
深入浅出：三大支柱如何影响AI性能
模型大小（Model Size - N）：
- 比喻：就像一个人的“脑容量”或者“知识架构”。一个参数量巨大的模型，拥有更多的神经元和连接，意味着它能学习和存储更复杂的模式、更丰富的知识。
- 现实：参数量通常以亿、千亿甚至万亿计。例如，GPT-3就是以其1750亿参数而闻名，这些庞大的参数量让模型能够捕捉到语言中极为细微的关联。
数据集大小（Dataset Size - D）：
- 比喻：相当于一个人“阅读过的书籍总量”或“经历过的事情总数”。模型学到的数据越多，它对世界的理解就越全面，越能举一反三。高质量、多样化的数据至关重要。
- 现实：大型语言模型通常在万亿级别的文本数据上进行训练，这些数据来源于互联网、书籍、论文等，让模型拥有广阔的“知识面”。
计算资源（Compute Budget - C）：
- 比喻：这代表了“学习的努力程度”和“学习工具的先进性”。强大的GPU集群和足够长的训练时间，就像是超级大脑加速器，让模型能更快、更透彻地从海量数据中学习和提炼知识。
- 现实：训练一次大型语言模型可能需要数百万美元的计算成本，耗费数月时间，涉及成千上万块高性能图形处理器（GPU）的协同工作。
卡普兰缩放定律的核心表明，这三者并非线性叠加，而是以一种“事半功倍”的方式相互作用。例如，当你将模型做大10倍，性能提升可能远不止10倍，甚至会涌现出新的能力。这种预测性让AI研究者能够有方向地优化资源分配，预估未来模型的性能边界。
缩放定律的演进：从卡普兰到Chinchilla
最初的卡普兰缩放定律在2020年提出时，倾向于认为在给定预算下，增加模型大小能带来更大的性能提升。然而，随着研究的深入，DeepMind在2022年提出了“Chinchilla缩放定律”，对此进行了重要的补充和修正。Chinchilla研究发现，对于给定的计算预算，存在一个模型大小和数据集大小的最优平衡点，而不是一味地增大模型。它指出，最优的训练数据集大小大约是模型参数数量的20倍。
打个比方，卡普兰定律可能更像是在说“厨师越厉害越好”，而Chinchilla定律则告诉我们：“再厉害的厨师，也得配上足够多的好食材，才能发挥最佳水平，不能只顾着请大厨而忽略了备料。” 这两个定律共同构成了我们理解当下大型AI模型如何成长和优化的重要基石。
为什么缩放定律如此重要？
- 指明了方向：它不像过去AI发展那样依赖于灵光一现的算法突破，而是揭示了一条通过系统性地增加资源投入，就能“按图索骥”地提升AI智能水平的清晰路径。
- 解释了“涌现能力”：当模型规模达到一定程度时，它们会展现出一些在小模型上不曾出现的能力，比如进行复杂推理、生成创意文本等，这些被称为“涌现能力”（Emergent Abilities）。缩放定律为理解这些能力的出现提供了理论基础。
- 推动了AGI（通用人工智能）的探索：缩放定律的存在，让人们对通过持续放大模型、数据和计算来最终实现通用人工智能（AGI）充满了信心和期待。
总之，“卡普兰缩放定律”以及后续的“Chinchilla缩放定律”就像AI领域的一盏明灯，它不是告诉你AI是什么，而是告诉你AI是如何变得如此强大，以及未来还有多大的潜力。它让我们明白，今天的AI成就，是在遵循着一套可预测的“增长秘籍”稳步前进的。
Kaplan Scaling: The Hidden Law Behind AI Growth
When we talk about Artificial Intelligence (AI), especially the shockwaves caused by Large Language Models (LLMs) like ChatGPT in recent years, there is a profound law silently supporting all this progress. It is the “Kaplan Scaling Law” (often referred to as part of the “Scaling Laws”) proposed by OpenAI researcher Jared Kaplan and his team in 2020. This law reveals the “secret” of AI model performance improvement, allowing us to predict and guide the development of AI in an unprecedented way.
What is the “Kaplan Scaling Law”? — The “Growth Guide” of the AI World
Imagine you are preparing for a major cooking competition. To make the most delicious dishes, you need to consider several key factors:
- Chef’s Ability (Model Size): An experienced chef (a model with many parameters) can usually make more complex dishes and handle various ingredients.
- Quality and Quantity of Ingredients (Dataset Size): Even the best chef cannot make a meal without rice—sufficient and fresh ingredients (high-quality, large-scale data) are essential.
- Kitchen Equipment and Time Invested (Compute Resources): Having top-tier equipment and ample time to practice and debug allows the chef to fully utilize their skills (high computing power, long training time).
The “Kaplan Scaling Law” acts like the “growth guide” for this cooking competition. It points out that the performance of AI models (e.g., the probability of the model making errors or its ability to understand language) does not improve steadily by chance but has a predictable power-law relationship with these three core factors: Model Size (Parameters), Dataset Size, and Compute Resources consumed during training. Simply put, as long as we continuously and strategically increase these three “inputs,” the performance of AI models will continue to improve in a predictable manner.
Jared Kaplan himself was a theoretical physicist. He examined AI with the rigorous perspective of a physicist and found that the development of AI also follows precise mathematical laws like physics laws, as if he had found the “Law of Universal Gravitation” in the field of AI.
Deep Dive: How the Three Pillars Affect AI Performance
Model Size (N):
- Analogy: Like a person’s “brain capacity” or “knowledge architecture.” A model with a huge number of parameters has more neurons and connections, meaning it can learn and store more complex patterns and richer knowledge.
- Reality: Parameter counts are usually measured in billions, hundreds of billions, or even trillions. For example, GPT-3 is famous for its 175 billion parameters, allowing the model to capture extremely subtle associations in language.
Dataset Size (D):
- Analogy: Equivalent to the “total number of books read” or “total number of experiences” of a person. The more data a model learns, the more comprehensive its understanding of the world, and the better it can draw inferences. High-quality, diverse data is crucial.
- Reality: Large language models are typically trained on trillions of text data tokens sourced from the internet, books, papers, etc., giving the model a vast “scope of knowledge.”
Compute Budget (C):
- Analogy: This represents the “effort of learning” and the “advanced nature of learning tools.” Powerful GPU clusters and long enough training time are like super-brain accelerators, allowing the model to learn and extract knowledge from massive data faster and more thoroughly.
- Reality: Training a large language model once can cost millions of dollars in computing costs, take months, and involve the collaborative work of thousands of high-performance Graphics Processing Units (GPUs).
The core of Kaplan Scaling Law indicates that these three are not linearly additive but interact in a “multiplier effect” way. For example, when you increase the model size by 10 times, the performance improvement may be far more than just “better,” and new capabilities may even emerge. This predictability allows AI researchers to allocate resources with direction and estimate the performance boundaries of future models.
Evolution of Scaling Laws: From Kaplan to Chinchilla
When the original Kaplan Scaling Law was proposed in 2020, it tended to suggest that increasing model size brought greater performance gains for a given budget. However, as research deepened, DeepMind proposed the “Chinchilla Scaling Law” in 2022, which made important additions and corrections to this. Chinchilla research found that for a given compute budget, there is an optimal balance point between model size and dataset size, rather than blindly increasing the model size. It points out that the optimal training dataset size is about 20 times the number of model parameters.
To use an analogy, Kaplan’s Law might be more like saying “the more skilled the chef, the better,” while Chinchilla’s Law tells us: “No matter how skilled the chef is, they must be paired with enough good ingredients to perform at their best; you can’t just hire a big chef and ignore the preparation of ingredients.” These two laws together form an important cornerstone for our understanding of how current large-scale AI models grow and optimize.
Why are Scaling Laws So Important?
- Pointing the Direction: Unlike past AI development that relied on flashes of algorithmic breakthroughs, it reveals a clear path to improving AI intelligence systematically by increasing resource investment.
- Explaining “Emergent Abilities”: When the model scale reaches a certain level, they will show some capabilities that did not appear in small models, such as complex reasoning, generating creative text, etc. These are called “Emergent Abilities.” Scaling laws provide a theoretical basis for understanding the appearance of these capabilities.
- Driving the Exploration of AGI (Artificial General Intelligence): The existence of scaling laws gives people confidence and expectation that AGI can eventually be achieved by continuously scaling up models, data, and computation.
In short, “Kaplan Scaling Law” and the subsequent “Chinchilla Scaling Law” are like a beacon in the field of AI. It doesn’t tell you what AI is, but how AI becomes so powerful and how much potential lies in the future. It makes us understand that today’s AI achievements are moving forward steadily following a predictable “growth guide.”