The code behind the picture

3 teaching cells · Python standard library · Read-only

1. 1. Prepare the inputs

   Both schedules use 1000 steps. Step 0 is the clean picture, so its cumulative product is 1.

   In [ ]:

   import json
   import math
   
   T = 1000
   steps = [250, 500]
   s = 0.008

2. 2. Build both schedules

   Each step keeps 1 − β of what was there; ᾱ is the running product of those keeps. The cosine β is capped at 0.999.

   In [ ]:

   def f(t):
       return math.cos(((t / T + s) / (1 + s)) * math.pi / 2) ** 2
   
   def linear(t):
       return 0.0001 + (0.02 - 0.0001) * (t - 1) / (T - 1)
   
   def cosine(t):
       return min(1 - f(t) / f(t - 1), 0.999)
   
   def alpha_bar(beta):
       out = [1.0]
       for t in range(1, T + 1):
           out.append(out[-1] * (1 - beta(t)))
       return out

3. 3. Read the picture weights

   The picture weight at step t is √ᾱₜ. Print it for both schedules at the same steps.

   In [ ]:

   result = {
       name: [round(math.sqrt(alpha_bar(beta)[t]), 6) for t in steps]
       for name, beta in [("linear", linear), ("cosine", cosine)]
   }
   print(json.dumps(result))

{
  "linear": [
    0.723937,
    0.280334
  ],
  "cosine": [
    0.920333,
    0.70274
  ]
}