PARAMETERS
参数规模Parameters
模型容量轴；单独增大可能吃不满。The capacity axis; increasing it alone can leave capacity underused.
01 · 厨房扩十倍，食材与火力不变01 · Ten times the kitchen, same ingredients and heat
只把参数规模拉高，却不给更多数据与算力，这台更大的模型为什么可能只是“更大的空厨房”？If parameters grow while data and compute stay fixed, why can a larger model become little more than a bigger empty kitchen?
02在 3D 参数—数据—算力预算面上移动配置，失衡点自动标红Move a Configuration on the 3D Parameter–Data–Compute Budget Surface
3D 预算面 · 三轴配平3D budget surface · three-way balance
总预算指数Budget index
173
P + D + C
预测损失Predicted loss
1.12
toy L(P,D,C)
配置状态Configuration
BALANCED
three-way allocation
正在装载本地 3D 场景…若持续显示，需要 WebGL /
three.js 未加载。Loading the local 3D scene… If this remains visible, WebGL is
required or three.js did not load.
P 55 · D 60 · C 58
拖拽旋转 · 滚轮缩放 · 停手后缓转drag to orbit · wheel to zoom · idle auto-rotate
03把刚才的变化拆成 4 个零件Break the Change into Four Parts
Scaling LawsDATA
数据量Data
训练信号轴；不足会让大模型反复看少量样本。The signal axis; too little data makes a large model recycle few examples.
COMPUTE
计算预算Compute
把参数与数据真正用于更新的训练工作量。Training work that actually combines parameters and data.
BALANCE
经验配平Empirical balance
同预算面上，三者配比决定预测损失。On one budget surface, allocation among all three shapes predicted loss.
04最小机制：主交互能逐项验证Minimal Mechanism: Verify Each Link in the Interaction
MECHANISM
L(P,D,C) ≈ L∞ + aP−α + bD−β + compute_gap
三轴滑块共同定位一个配置点；与等预算面上的配平点距离越大，玩具预测损失越高并标红。The three sliders locate one configuration. Greater distance from
the balanced region on the equal-budget surface raises toy
predicted loss and turns the marker red.
设总预算Set budget形成等预算面form an equal-budget surface
分配 P / D / CAllocate P / D / C配置点落在面上或偏离place or miss the surface
比较经验损失Compare loss配平优于单轴堆叠balance beats one-axis scaling
05只把参数拉满，数据与算力保持低位Max Out Parameters While Data and Compute Stay Low
主动制造失败Create a failure边界实验Boundary experiment
红点看起来“模型更大”，但它远离配平区；玩具损失反而上升，说明缩放定律不是只看参数。The red point is a larger model, yet far from the balanced region. Toy loss rises, showing that scaling laws are not parameter-only rules.
尚未执行。先在主交互中观察正常机制。Not run yet. Observe the normal mechanism in the main interaction
first.
✗ 参数越多，损失必然越低。More parameters always lower loss.→ ✓ 数据与算力不足会让容量无法兑现。Insufficient data and compute can leave capacity
unrealized.
✗ 缩放定律是每个模型都精确成立的物理定律。Scaling laws are exact physical laws for every
model.→ ✓ 它们是特定范围与设置下的经验关系。They are empirical relationships for particular regimes and
setups.
✗ 预算面上的最优点永远不变。The optimum on a budget surface never moves.→ ✓ 架构、数据质量与硬件会改变经验系数。Architecture, data quality, and hardware change the empirical
coefficients.
06 · 一句话带走06 · One line to keep