Ask what should change when the equation is manipulated, then let the visualization test that expectation.
Foundation Lab
Label Smoothing & Soft Targets
Used in most vision models and LLMs—simple trick with consistent improvements
#60Label SmoothOptimization
key equation
y_{smooth} = (1 - \alpha) y + \frac{\alpha}{K}Selected Foundation Object
Keep the equation fixed; move through the evidence.
Concept 60 of 100Label SmoothOptimization / Phase 3: Optimization & generalization
Current question
Hard targets say "100% sure it's class 3"—but that's almost never true in real data
y_{smooth} = (1 - \alpha) y + \frac{\alpha}{K}Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
Use prerequisites, dependents, and semantic links to repair the next gap without leaving the object behind.
Why It Matters for Modern Models
- Used in most vision models and LLMs—simple trick with consistent improvements
- Prevents overconfidence, which improves calibration and sometimes generalization
- Knowledge distillation uses the same idea: train on soft targets from a teacher model
What Tutorials Skip
What is still poorly explained in textbooks and papers:
- Hard targets say "100% sure it's class 3"—but that's almost never true in real data
- Label smoothing implicitly regularizes: model can't drive logits to ±∞
- Connects to calibration: smoothed models give more honest uncertainty estimates
Interactive Visualization
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.
Key Equation
Instead of hard targets , use soft targets:
For and classes:
Effect on cross-entropy:
where is uniform. This penalizes overconfidence: logits can't go to infinity.